Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
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Page xv
... angle , nor that the equal sides are opposite to equal angles , nor , lastly , that things equal to the same thing are equal to one another ? By a scientific mind this information will not be thought lightly of ; and it is exactly that ...
... angle , nor that the equal sides are opposite to equal angles , nor , lastly , that things equal to the same thing are equal to one another ? By a scientific mind this information will not be thought lightly of ; and it is exactly that ...
Page 23
... equal to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each ... angles contained by those sides equal to one another , their bases , or third sides , shall be equal ; and the ...
... equal to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each ... angles contained by those sides equal to one another , their bases , or third sides , shall be equal ; and the ...
Page 24
... equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ...
... equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC ... angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ...
Page 25
... equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles are equal , to which the equal sides are opposite ; therefore ...
... equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles are equal , to which the equal sides are opposite ; therefore ...
Page 26
... equal to one another . Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of ... angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one ano- ther but the angle ECD is ...
... equal to one another . Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of ... angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one ano- ther but the angle ECD is ...
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Common terms and phrases
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore